Dimension reduction for compressible Navier–Stokes equations with density-dependent viscosity

Compressible Flows with a Density-Dependent Viscosity Coefficient

We prove the global existence of weak solutions for the 2-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient (λ = λ(ρ)). Initial data and solutions are small in energy-norm with nonnegative densities having arbitrarily large sup-norm. Then, we show that if there is a vacuum domain at the initial time, then the vacuum domain will retain for all time, and vanish...

Global solutions of compressible Navier–Stokes equations with a density–dependent viscosity coefficient

We prove the global existence and uniqueness of the classical (weak) solution for the 2D or 3D compressible Navier–Stokes equations with a density–dependent viscosity coefficient (λ = λ(ρ)). Initial data and solutions are only small in the energy-norm. We also give a description of the large time behavior of the solution. Then, we study the propagation of singularities in solutions. We obtain t...

Global Solutions to the Spherically Symmetric Compressible Navier-Stokes Equations with Density-Dependent Viscosity

We consider the exterior problem and the initial boundary value problem for the spherically symmetric isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficient in this paper. For regular initial density, we show that there exists a unique global strong solution to the exterior problem or the initial boundary value problem, respectively. In particular, the stro...

Decay rate of the compressible Navier-Stokes equations with density-dependent viscosity coefficients

Vacuum Behaviors around Rarefaction Waves to 1D Compressible Navier-Stokes Equations with Density-Dependent Viscosity

In this paper, we study the large time asymptotic behavior toward rarefaction waves for solutions to the 1-dimensional compressible Navier-Stokes equations with density-dependent viscosities for general initial data whose far fields are connected by a rarefaction wave to the corresponding Euler equations with one end state being vacuum. First, a global-in-time weak solution around the rarefacti...